The ∞-Fucík spectrum

In this article we study the behavior as p ↗ +∞ of the Fučik spectrum for p- Laplace operator with zero Dirichlet boundary conditions in a bounded domain ω sub; Rn. We characterize the limit equation, and we provide a description of the limit spectrum. Furthermore, we show some explicit computations of the spectrum for certain configurations of the domain.Fil: Rossi, Julio Daniel. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; ArgentinaFil: Salort, Ariel Martin. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Da Silva, Joao Vitor. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentin

The ∞-fučík spectrum

In this article we study the behavior as p % +∞ of the Fučik spectrum for pLaplace operator with zero Dirichlet boundary conditions in a bounded domain Ω ⊂ Rn. We characterize the limit equation, and we provide a description of the limit spectrum. Furthermore, we show some explicit computations of the spectrum for certain configurations of the domainFil: Rossi, Julio Daniel. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaFil: Salort, Ariel Martin. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; ArgentinaFil: Da Silva, Joao Vitor. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentin

On the solvability of Dirichlet problem for the weighted p-Laplacian

The paper investigates the existence and uniqueness of weak solutions for a non-linear boundary value problem involving the weighted $p$-Laplacian. Our approach is based on variational principles and representation properties of the associated spaces

Nutrient Balance from Agricultural Pollution Sources on Selected Tributaries to the Švihov Reservoir

Agriculture is the leading source of non-point sources of water pollution, especially in terms of the runoff process. Agricultural management promotes extensive water contamination, soil erosion and sedimentation in streams and reservoirs. The water reservoir Švihov on the Želivka river supplies drinking water to more than 1.5 million people. The catchment area of the water supply reservoir is intensively used for agriculture, more than 55% of the catchment area is arable land. Nutrients such as phosphorus and nitrates in the upper water-ways of tributaries are a huge problem. The aim of the research is to evaluate concentration trends and losses of nutrients (nitrates and phosphorus) at the chosen tributaries to the Švihov reservoir during 2018-2021. From the data on monthly concentrations and monthly discharges the monthly and annual losses of nitrates and phosphorus on each profile were calculated. The effect of discharges and concentrations on the magnitude of losses was investigated by correlation analysis. The influence of the forebay Trnávka dam on the magnitude of nutrient losses was also evaluated. The results show the importance of discharge magnitude on nutrient losses. The Trnávka forebay dam significantly reduces the transport of phosphorus from the Trnava catchment to the Švihov reservoir. In the catchment area of the reservoir it is recommended to implement nature-friendly and technical measures for water retention and accumulation in the landscape in order to reduce nutrient transport.O